Computer modelling research has undermined the view that double dissociations in behaviour are sufficient to infer separability in the cognitive mechanisms underlying those behaviours. However, all these models employ "multi-modal" representational schemes, where functional specialisation of processing emerges from the training process. Targeted lesioning of different regions of functional specialisation leads to varied but predictable deficits in model performance. We argue that multi-modal representational schemes are not a necessary condition for the observation of double dissociations in an information processing system that shares resources across multiple tasks. Using a "uni-modal" representational system, we demonstrate that double dissociations may also result from stochastic processes. Lesioning experiments on a single-route, uni-modal connectionist model of regular and irregular noun and verb morphology confirm and extend earlier work demonstrating that selective impairment across tasks can result from damage to a distributed information processing system. A systematic investigation of the degree to which performance deteriorates across different inflectional classes reveals that simple and double dissociations can occur in this single-route, uni-modal model. An important prediction of the model is that double dissociations between regular and irregular inflection, resulting from stochastic processes should be extremely rare. However, they are particularly likely to occur when the researcher uses test batteries consisting of a small number of items. Given that cognitive neuropsychologists rarely provide details about the distribution of performance in a disordered population, it is concluded that a stochastic interpretation of double dissociations may have wider applicability than is normally supposed.